how do we find the area of parallelograms, kites and trapezoids?

How Do We Find The Area of Parallelograms, Kites and Trapezoids?

 

 

Trapezoid

a quadrilateral with exactly one pair of parallel sides

Area= (b1+b2)/2(h)

 

 

 

http://www.mathwarehouse.com/geometry/quadrilaterals/trapezoid/picture-of-trapezoid.gif

 

 

 

 

Kites

two pairs of consecutive congruent sides

Area= d1d2/2

 

 

 

http://www.wyzant.com/Images/Help/trap_kite6.gif

 

 

 

 

 

 



how do we identify solids?

How Do We Identify Solids?

 

Solid Geometry

The geometry of 3 dimensional space

-3 dimensions (3D)- width, depth, and height

 

 

 

 

http://www.gotoandplay.it/_articles/2004/07/3dCube/cube.gif

 

 

Properties

Solids have properties such as:

-volume (think of how much water it could hold)

- surface area (thinks of the area you would have to paint)

 

Two types of solids, "polyhedral", and "non-polyhedral"

 

Polyhedra

They must have flat faces

 

Prism

Has the same cross section all along it's length

http://www.mathsteacher.com.au/year7/ch09_polygons/06_polyhedra/Image11220.gif

 

 

 

Pyramids

 

 

http://www.mathsisfun.com/geometry/images/pyramid-height-perimeter.jpg

 

 

Non- Polyhedra

Any surface that isn't flat

examples:

 

Sphere

 

http://etc.usf.edu/clipart/41700/41749/FC_Sphere_41749_lg.gif

 

 

 

 

 

Torus

 

 

 http://www.math.cornell.edu/~mec/2003-2004/geometry/torii/torus.jpg

 

 

Cylinders

 

http://upload.wikimedia.org/wikipedia/commons/thumb/3/36/Circular_cylinder_rh.svg/220px-Circular_cylinder_rh.svg.png

 

 

 

 

 

Cone

 

http://accad.osu.edu/~pgerstma/class/vnv/resources/info/AnnotatedVrmlRef/Images/Cone.gif

 

 

Cross sections

The shape you get when cutting straight across an object

 

 

Surface Area

Area of the bases + lateral area (area of the sides)

 



 

 



How Do We Use Conjunctions and Disjunctions?

 

 

Conjunctions:

Hooking up words and phrases and clauses with AND.

- Has two statements connected by AND

 

 

Disjunctions:

Hooking up words and phrases and clauses with OR

- Has two statements connected by OR

 

 

Conditional:

The most frequently used statement in the construction or an argument or in the study of mathematics

       -Conditional- "if" (hypothesis), "then" (conclusion)

       - Inverse- Negate "if", "then"

       - Converse- switch "if", "then"

       - Contrapositive- Negate the converse 

How Do We Use Contrapositives?

 

Contrapositives:

Contra- prefix meaning "against" or "opposite"

you negate AND switch the hypothesis and conclusion (inverse and converse)

 

 

Examples:

1. "If I study, then I'll pass geometry." = "If I don't pass geometry, then I didn't study."

     2.  "If I am tired. then I will go to sleep." = "If I don't go to sleep, then I am not tired."

 

The "if" and "then" don't change with the hypothesis and the conclusion.

   

     3. "If Lisa sells the house, than her income will not remain the same." = "If her income does stay the same, then Lisa won't sell the house."

    

    4. "If a number is divisible by six, than it is divisible by three." = "If a number isn't divisible three, then it isn't divisible by six."

how do we use circle equations to solve problems?

How Do We Use Circle Equations to Solve Problems?

What is the midpoint?

(5,2) and (-3,-4)                          -4+2=-2

5+-3=2                                         -2/2=-1

2/2=1                                           -1=y

1=x

m=(1,-1)

What is the distance from (1,-1) to (5,2)?

d= (5-1)^2+ (2+1)^2

d= 16+9

d= 25

d=5

how do we define circles?

How Do We Define Circles?

Circle

A circle is the set of all points in a plane at given distance froma given point.

http://www.math.com/school/subject3/lessons/S3U1L6GL.html

-Given distance is the radius

- point is called the center

Chord

A line segment that connects two points on a circle 

http://en.wikibooks.org/wiki/Geometry/Chapter_7

Diameter

A line segment through the center with endpoints on the circle

http://openhighschoolcourses.org/mod/book/view.php?id=258&chapterid=500

Tangent

A line that touches a circle in exactly one point.

http://www.icoachmath.com/math_dictionary/Common_External_Tangent.html

-Congruent circles have the same radius

-Concentric circles have the same center

Semicircle

half a circle= 180 degrees

Minor Arch- less than 180 degrees

Major Arch- more than 180 degrees

what are the special parallelograms?

What Are The Special Parallelograms?

Rhombus

A parallelogram with four congruent sides.

http://math.tutorvista.com/geometry/quadrilaterals.html



In the example above, the diagonals bisect the angles and they also bisect each other.



Rectangle

Parallelogram with four congruent angles or an "equiangular parallelogram."

http://www.geom.uiuc.edu/~dwiggins/conj28.html

The diagonals of a rectangle are congruent and they bisect each other.

Equilateral Rectangle

Equiangular rhombus

http://quizlet.com/6547298/geometry-terms-cfh-flash-cards/

Diagonals are congruent, perpendicular and they bisect each other.